Happened to my party member and I, except we'd engage and hit it a couple of times, then it would practically destroy us while we stood there not being able to hit back. It just kept going on and on about "target is already engaged."

Go into passive mode - the mob will go from name in purple (engaged by someone else) to white (free to attack) From that point you should be able to engage again. The name will now go red as it is engaged as your target.